A national park has a current population of 2000 bison. They reproduce annually at a rate of 5%. Experts say the park can sustain a population of 10,000 bison. What is the current population 30 years from now?

This problem describes logistic growth, which models populations that grow rapidly at first but slow down as they approach a carrying capacity (in this case, 10,000 bison). The logistic growth model is given by:

\[
P(t) = \frac{K}{1 + \left( \frac{K - P_0}{P_0} \right) e^{-rt}}
\]

Where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population (2000 bison),
- \( K \) is the carrying capacity (10,000 bison),
- \( r \) is the growth rate (5% or 0.05),
- \( t \) is the time in years (30 years).

Let's calculate the population 30 years from now using this formula.The projected bison population in the national park 30 years from now is approximately 5,284.

Would you like more details on the logistic growth process or the formula used?

Here are some related questions to explore:
1. What would the population be after 50 years?
2. How does the population change if the growth rate increases to 8%?
3. What is the population after 10 years with the same growth rate?
4. How many years will it take for the population to reach 9,000 bison?
5. What happens to the population if the carrying capacity is reduced to 8,000?

**Tip:** Logistic growth is useful for modeling populations in environments with limited resources, preventing exponential growth forever.

Learn how to calculate the population of bison in a national park after 30 years using the logistic growth model. This problem explores concepts like population dynamics, logistic growth, and carrying capacity, with a specific focus on the reproduction rate of 5% and a maximum sustainable population of 10,000 bison.

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